Finite Group Databasebeta

← #14564699

Subgroups — #14564699

Order 2432.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927051C212yesmaximal, complemented
2#11926561C212yesmaximal, complemented
3#11926507C211yesmaximal, characteristic, complemented
4#11926301C211yesmaximal, characteristic, complemented
5C19×#575C211yesmaximal, characteristic, complemented
6C2×#41×C19C2212yes—
7C22×C4×D19C2211yescharacteristic
8C19×#137—22no—
9C19×AGL(1,ℤ/8)—22no—
10C19×#135—22no—
11C2×M16×C19C2211yescharacteristic
12#10597392—22no—
13#10597384—22no—
14#10597383—22no—
15#10597381—22no—
16C4×C22⋊D19—24no—
17#10597372C2212yes—
18C2×#64520C2211yescharacteristic
19#10597294—24no—
20(C2×D19)⋊C8—22no—
21C23×D19D411yescharacteristic
22#41×C19—22no—
23#41×C19—22no—
24#41×C19—22no—
25#41×C19—22no—
26C2×Q8×C19D412yescomplemented
27C2×D4×C19—22no—
28C2×D4×C19D412yescomplemented
29C22×C4×C19—22no—
30C22×C4×C19C2311yescharacteristic
31C2×C22⋊D19—24no—
32C22×Dic19D411yescharacteristic
33C2×C4×D19—22no—
34C2×C4×D19—21no—
35C2×C4×D19—22no—
36C2×C4×D19—21no—
37Q16×C19—22no—
38SD16×C19—24no—
39D8×C19—22no—
40M16×C19—22no—
41C2×C8×C19D412yescomplemented
42C22⋊Dic19—24no—
43C22⋊Dic19—22no—
44(C2×D19)⋊C4—24no—
45C4⋊Dic19—22no—
46Dic19⋊C4—24no—
47C4×Dic19D414yescomplemented
48#64520—22no—
49C2×C19⋊C8—21no—
50C23×C19—22no—
51C23×C19C2×D411yescharacteristic
52C22×D19—22no—
53C22×D19—21no—
54C22×D19—42no—
55Q8×C19—22no—
56Q8×C19—22no—
57D4×C19—22no—
58D4×C19—22no—
59D4×C19—42no—
60D4×C19—42no—
61C2×C4×C19—22no—
62C2×C4×C19—42no—
63C2×C4×C19—42no—
64C2×C4×C19C2×D412yes—
65C2×C4×C19C2×D412yes—
66C2×C4×C19C2×D411yescharacteristic
67C2×C4×C19#4111yescharacteristic
68C22⋊D19—48no—
69C2×Dic19—24no—
70C2×Dic19—22no—
71C2×Dic19—21no—
72C4×D19—41no—
73C4×D19—42no—
74C4×D19—41no—
75C8×C19—22no—
76C19⋊C8—41no—
77#2010—191nomaximal, Sylow
78C22×C19—41no—
79C22×C19—44no—
80C22×C19—42no—
81C22×C19#12012yes—
82C22×C19#12111yescharacteristic
83C2×D19—24no—
84C2×D19—22no—
85C2×D19—42no—
86C2×D19—41no—
87C2×D19—41no—
88C4×C19—42no—
89C4×C19#12011yescharacteristic
90C4×C19#12112yes—
91C4×C19#12711yescharacteristic
92Dic19—44no—
93Dic19—41no—
94#575D1911yescharacteristic, complemented
95#525—192no—
96#421—192no—
97#407—191no—
98H(3,ℤ/4)—191no—
99C2×C19—22no—
100C2×C19—21no—
101C2×C19—82no—
102C2×C19#39211yescharacteristic
103D19—42no—
104C2×#41C2×D1912yes—
105C23×C4—191no—
106#137—22no—
107AGL(1,ℤ/8)—22no—
108#135—22no—
109C2×M16—191no—
110C2×M16C2×D1911yescharacteristic
111#123—382no—
112C22⋊Q8—382no—
113#121—382no—
114#120—382no—
115C4×D4—384no—
116#117—192no—
117#104—384no—
118C22⋊C8—382no—
119C19#201011yescharacteristic, complemented, Sylow
120C24—191no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D1912yescomplemented
126C2×D4—22no—
127C2×D4—384no—
128C2×D4C22⋊D1912yescomplemented
129C22×C4—22no—
130C22×C4—191no—
131C22×C4—382no—
132C22×C4—381no—
133C22×C4—381no—
134C22×C4—382no—
135C22×C4C22×D1911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—382no—
141C2×C8—381no—
142C2×C8C22⋊D1912yescomplemented
143C4⋊C4—384no—
144C4⋊C4—382no—
145C22⋊C4—384no—
146C22⋊C4—384no—
147C22⋊C4—382no—
148C42—194no—
149C23—22no—
150C23—382no—
151C23—381no—
152C23—762no—
153C23D4×D1911yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—768no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—384no—
165C2×C4—382no—
166C2×C4—381no—
167C2×C4—762no—
168C2×C4—761no—
169C2×C4—761no—
170C2×C4D4×D1912yes—
171C2×C4#6454311yescharacteristic
172C2×C4C2×C22⋊D1912yes—
173C2×C4C2×C22⋊D1911yescharacteristic
174C8—22no—
175C8—761no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—384no—
180C22—382no—
181C22—762no—
182C22—761no—
183C22—761no—
184C22#1059738312yes—
185C22#1059738411yescharacteristic
186C4—42no—
187C4—764no—
188C4—761no—
189C4#1059738512yes—
190C4#1059738611yescharacteristic
191C4#1059739911yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—762no—
196C2#1192645211yescharacteristic
subgroupG/H
centerC4#10597386
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#575C2
socleC2×C19#392
hypercenter#575D19
hypocenterC19#2010
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11927051C2semidirect
2. #11926561C2semidirect
3. #11926507C2semidirect
4. #11926301C2semidirect
5. C19×#575C2semidirect
26. C2×Q8×C19D4semidirect
28. C2×D4×C19D4semidirect
41. C2×C8×C19D4semidirect
47. C4×Dic19D4semidirect
94. #575D19semidirect
119. C19#2010semidirect
125. C2×Q8C22⋊D19semidirect
128. C2×D4C22⋊D19semidirect
142. C2×C8C22⋊D19semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#119270512
#119265612
#119265072
#119263012
C19×#5752
#201019